U.S. patent number 9,871,584 [Application Number 15/028,619] was granted by the patent office on 2018-01-16 for method of characterizing a multimode optical fiber link and corresponding methods of fabricating multimode optical fiber links and of selecting multimode optical fibers from a batch of multimode optical fibers.
This patent grant is currently assigned to Draka Comteq, B.V.. The grantee listed for this patent is Draka Comteq B.V.. Invention is credited to Marianne Bigot-Astruc, Denis Molin, Pierre Sillard.
United States Patent |
9,871,584 |
Molin , et al. |
January 16, 2018 |
**Please see images for:
( Certificate of Correction ) ** |
Method of characterizing a multimode optical fiber link and
corresponding methods of fabricating multimode optical fiber links
and of selecting multimode optical fibers from a batch of multimode
optical fibers
Abstract
The invention concerns a method of characterizing a multimode
optical fiber link comprising a light source and a multimode fiber,
which comprises: a step (170) of characterizing the multimode fiber
using a measurement of the Dispersion Modal Delay (DMD) and
delivering fiber characteristic data; a step (171) of
characterizing the light source by at least three source
characteristic curves showing three parameters of the source as a
function of a fiber radius r and obtained by a technique similar to
the DMD measurement; a step (173) of computing an Effective
Bandwidth (EB) of the link, comprising calculating (172) a transfer
function using both the fiber characteristic data and each of said
source characteristic curves.
Inventors: |
Molin; Denis (Draveil,
FR), Sillard; Pierre (Le Chesnay, FR),
Bigot-Astruc; Marianne (Janvry, FR) |
Applicant: |
Name |
City |
State |
Country |
Type |
Draka Comteq B.V. |
Amsterdam |
N/A |
NL |
|
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Assignee: |
Draka Comteq, B.V. (Amsterdam,
NL)
|
Family
ID: |
50288186 |
Appl.
No.: |
15/028,619 |
Filed: |
October 15, 2013 |
PCT
Filed: |
October 15, 2013 |
PCT No.: |
PCT/IB2013/002806 |
371(c)(1),(2),(4) Date: |
April 11, 2016 |
PCT
Pub. No.: |
WO2015/056044 |
PCT
Pub. Date: |
April 23, 2015 |
Prior Publication Data
|
|
|
|
Document
Identifier |
Publication Date |
|
US 20160254861 A1 |
Sep 1, 2016 |
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04B
10/07951 (20130101); H04B 10/0731 (20130101); G01M
11/338 (20130101); G01M 11/332 (20130101); H04B
10/2581 (20130101) |
Current International
Class: |
H04B
10/00 (20130101); H04B 10/079 (20130101); G01M
11/00 (20060101); H04B 10/073 (20130101); H04B
10/2581 (20130101) |
Field of
Search: |
;398/25-28 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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2144096 |
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Jan 2010 |
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EP |
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2207022 |
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Jul 2010 |
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EP |
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2584388 |
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Apr 2013 |
|
EP |
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2010/147841 |
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Dec 2010 |
|
WO |
|
2015/056044 |
|
Apr 2015 |
|
WO |
|
Other References
International Preliminary Report on Patentability in counterpart
International Application No. PCT/IB2013/002806 dated Apr. 19,
2016, pp. 1-7 [All references previously cited]. cited by applicant
.
International Search Report in counterpart International
Application No. PCT/IB2013/002806 dated Jun. 27, 2014, pp. 1-3.
cited by applicant .
Sengupta, "Calculated Modal Bandwidths of an OM4 Fiber and the
Theoretical Challenges" by International Wire & Cable
Symposium, Proceedings of the 581th IWCS/IICIT, pp. 24-29. cited by
applicant.
|
Primary Examiner: Bello; Agustin
Attorney, Agent or Firm: Additon, Higgins & Pendleton,
P.A.
Claims
The invention claimed is:
1. A method of characterizing a multimode optical fiber link
comprising a light source and at least one multimode fiber, said
method comprising a step of characterizing said multimode fiber
using a measurement of the Dispersion Modal Delay (DMD) and
delivering fiber characteristic data, characterized in that said
method also comprises: a step of characterizing said light source
by at least three source characteristic curves obtained by:
exciting a nominal multimode fiber with said light source; scanning
with a single mode fiber an output signal of said nominal multimode
fiber, at different radial offset values r, from an axis of said
nominal fiber where r=0 to a radial offset value r=a, where a is
the core radius of said nominal fiber, analyzing with a spectrum
analyzer an output optical spectrum of said single mode fiber for
each radial offset value r, said source characteristic curves each
showing a source parameter as a function of said radial offset
value r; a step of computing an Effective Bandwidth (EB) of said
link, comprising calculating a transfer function using both said
fiber characteristic data and each of said source characteristic
curves.
2. The method according to claim 1, wherein said source
characteristic curves comprise: a curve showing an output power
P(r) of said source as a function of said radial offset value r,
0.ltoreq.r.ltoreq.a; a curve showing a center wavelength
.lamda..sub.c(r) of said source as a function of said radial offset
value r, 0.ltoreq.r.ltoreq.a; a curve showing a root mean square
spectral width .DELTA..lamda.(r) of said source as a function of
said radial offset value r, 0.ltoreq.r.ltoreq.a.
3. The method according to claim 1, wherein said nominal multimode
fiber exhibits a length close to said link length.
4. The method according to claim 1, wherein said step of
characterizing said multimode fiber and said step of characterizing
said light source use the same single mode fiber.
5. The method according to claim 1, wherein said step of computing
an Effective Bandwidth (EB) of said link derives said Effective
Bandwidth from a transfer function H(f): where
.function..times..function..function..function..function..times..times..t-
imes..times..pi..times..times..DELTA..times..times..tau..function..times..-
sigma..function. ##EQU00017## with:
.DELTA..times..times..tau..times..lamda..function..lamda.
##EQU00018##
.sigma..function..DELTA..times..times..lamda..function..times.
##EQU00018.2## where: {tilde over (s)}.sub.DMD(r,f) and {tilde over
(s)}.sub.ref(f) are the Fourier transform of s.sub.DMD(r,t) and
s.sub.ref(t), L is the multimode fiber length in said link,
L.sub.DMD is a length of multimode fiber used in said measurement
of the Dispersion Modal Delay, D is the chromatic dispersion of
said nominal fiber expressed in ps/nm-km, .lamda..sub.DMD is the
wavelength of said measurement of the Dispersion Modal Delay,
s.sub.DMD(r,t) is a DMD trace at radial offset value r,
s.sub.ref(t) is a reference pulse signal, and OMBc(r) is the OMBc
(for "Overfilled Modal Bandwidth calculated") weight function.
6. The method according to claim 5, wherein said chromatic
dispersion D in .DELTA.r(r) is replaced by a function of the radius
D(r), such that:
.DELTA..tau.(r)=LD(r)(.lamda..sub.c(r)-.lamda..sub.DMD).
7. The method according to claim 6, wherein
D(r)=D.sub.0+ar.sup.2+br, where D.sub.0 a and b are coefficients
calculated using a method belonging to the group comprising:
chromatic dispersion measurements along radius with DMD like
excitations; comparing ROD curves obtained at two different
wavelengths.
8. The method according to claim 1, wherein said step of
characterizing said multimode fiber comprises a step of calculating
at least three fiber characteristic curves from said measurement of
said Dispersion Modal Delay, said fiber characteristic curves
comprising: a curve showing a Radial Offset Bandwidth ROB(r) of
said multimode fiber as a function of said radial offset value r,
0.ltoreq.r.ltoreq.a; a curve showing a Radial Offset Delay ROD(r)
of said multimode fiber as a function of said radial offset value
r, 0.ltoreq.r.ltoreq.a; a curve showing a Radial Coupling Power
P.sub.DMD(r) of said multimode fiber as a function of said radial
offset value r, 0.ltoreq.r.ltoreq.a.
9. The method according to claim 8, wherein said step of computing
an Effective Bandwidth (EB) of said link derives said Effective
Bandwidth from a transfer function H(f): where
.function..times..function..function..function..times..times..times..time-
s..pi..function..DELTA..times..times..tau..function..DELTA..times..times..-
tau..function..times..sigma..function..sigma..function.
##EQU00019## with:
.DELTA..times..times..tau..function..lamda..function..lamda.
##EQU00020##
.sigma..function..DELTA..times..times..lamda..function..times.
##EQU00020.2##
.DELTA..times..times..tau..function..intg..function..intg..function..abou-
t..times..times..times..times..function. ##EQU00020.3##
.sigma..function..times..times..times..times..function..times.
##EQU00020.4## where: L is the multimode fiber length in said link,
L.sub.DMD is a length of multimode fiber used in said measurement
of the Dispersion Modal Delay, D is the chromatic dispersion of
said nominal fiber expressed in ps/nm-km, .lamda..sub.DMD is the
wavelength of said measurement of the Dispersion Modal Delay,
s.sub.DMD(r,t) is a DMD trace at radial offset value r, and OMBc(r)
is the OMBc (for "Overfilled Modal Bandwidth calculated") weight
function.
10. The method according to claim 9, wherein said chromatic
dispersion D in .DELTA..tau.(r) is replaced by a function of the
radius D(r), such that:
.DELTA..tau.(r)=LD(r)(.lamda..sub.c(r)-.lamda..sub.DMD).
11. The method according to claim 10, wherein
D(r)=D.sub.0+ar.sup.2+br, where D.sub.0 a and b are coefficients
calculated using a method belonging to the group comprising:
chromatic dispersion measurements along radius with DMD like
excitations; comparing ROD curves obtained at two different
wavelengths.
12. The method of fabricating multimode optical fiber links
comprising a light source and a multimode fiber, the method
comprising: selecting a set of multimode optical fibers and a set
of light sources; for each multimode optical fiber and for each
light source in said sets, characterizing the multimode optical
fiber link formed with said multimode optical fiber and said light
source by (i) characterizing said multimode fiber using a
measurement of the Dispersion Modal Delay (DMD) and delivering
fiber characteristic data, (ii) characterizing said light source by
at least three source characteristic curves obtained by exciting a
nominal multimode fiber with said light source, scanning with a
single mode fiber an output signal of said nominal multimode fiber,
at different radial offset values r, from an axis of said nominal
fiber where r=0 to a radial offset value r=a, where a is the core
radius of said nominal fiber, and analyzing with a spectrum
analyzer an output optical spectrum of said single mode fiber for
each radial offset value r, wherein said source characteristic
curves each show a source parameter as a function of said radial
offset value r, and (iii) computing an Effective Bandwidth (EB) of
said link, comprising calculating a transfer function using both
said fiber characteristic data and each of said source
characteristic curves; selecting only those multimode optical fiber
links for which the effective bandwidth EB>3000 MHz-km.
13. The method according to claim 12, wherein said step of
selecting only those multimode optical fiber links for which the
effective bandwidth EB>3000 MHz-km comprises selecting only
those multimode optical fiber links for which the effective
bandwidth EB>4500 MHz-km.
14. The method according to claim 12, wherein said step of
selecting only those multimode optical fiber links for which the
effective bandwidth EB>3000 MHz-km comprises selecting only
those multimode optical fiber links for which the effective
bandwidth EB>6000 MHz-km.
15. The method of selecting multimode optical fibers from a batch
of multimode optical fibers, the method comprising: selecting a
batch of multimode optical fibers and a set of light source
metrics; for each multimode optical fiber and each light source
metric in said set, characterizing the multimode optical fiber link
formed with said multimode optical fiber and said light source
metric by (i) characterizing said multimode fiber using a
measurement of the Dispersion Modal Delay (DMD) and delivering
fiber characteristic data, (ii) characterizing said light source by
at least three source characteristic curves obtained by exciting a
nominal multimode fiber with said light source, scanning with a
single mode fiber an output signal of said nominal multimode fiber,
at different radial offset values r, from an axis of said nominal
fiber where r=0 to a radial offset value r=a, where a is the core
radius of said nominal fiber, and analyzing with a spectrum
analyzer an output optical spectrum of said single mode fiber for
each radial offset value r, wherein said source characteristic
curves each show a source parameter as a function of said radial
offset value r, and (iii) computing an Effective Bandwidth (EB) of
said link, comprising calculating a transfer function using both
said fiber characteristic data and each of said source
characteristic curves; selecting only those multimode optical
fibers for which the minimal calculated effective bandwidth over
the whole set of light source metrics is >3000 MHz-km, wherein
the set of light source metrics is obtained through measuring or
modeling a representative set of light sources.
16. The method according to claim 15, wherein said step of
selecting only those multimode optical fibers for which the minimal
calculated effective bandwidth over the whole set of light source
metrics is >3000 MHz-km comprises selecting only those multimode
optical fibers for which the minimal calculated effective bandwidth
over the whole set of light source metrics is >4500 MHz-km.
17. The method according to claim 15, wherein said step of
selecting only those multimode optical fibers for which the minimal
calculated effective bandwidth over the whole set of light source
metrics is >3000 MHz-km comprises selecting only those multimode
optical fibers for which the minimal calculated effective bandwidth
over the whole set of light source metrics is >6000 MHz-km.
Description
1. FIELD OF THE INVENTION
The present invention relates to the filed of optical fiber
transmissions, and more specifically, to multimode fibers used in
relative long reach and high bitrate systems. More specifically,
the invention relates to a method of characterizing a multimode
optical fiber link, comprising a light source and one or several
multimode fibers, used in such optical transmission systems.
2. BACKGROUND
Multimode fibers are successfully used in high-speed data networks
together with high-speed sources that are typically using
transversally multimode vertical cavity surface emitting lasers,
more simply called VCSELs.
The Effective Bandwidth drives the performance of a system
comprising a multimode fiber and a light source such as a VCSEL,
and allows assessing the highest bit rate achievable and/or the
longest reach achievable.
The Effective Bandwidth results from the combination of the modal
dispersion and the chromatic dispersion.
Modal dispersion results from the fact that, in a multimode fiber,
for a particular wavelength, several optical modes propagate
simultaneously along the fiber, carrying the same information, but
travelling with different propagation velocities. Modal dispersion
is expressed in terms of Differential Mode Delay (DMD), which is a
measure of the difference in pulse delay (ps/m) between the fastest
and slowest modes traversing the fiber.
In order to minimize modal dispersion, the multimode optical fibers
used in data communications generally comprise a core showing a
refractive index that decreases progressively going from the center
of the fiber to its junction with a cladding. In general, the index
profile is given by a relationship known as the ".alpha. profile",
as follows:
.function..times..times..DELTA..function..alpha..times..times..times..tim-
es..ltoreq. ##EQU00001##
where:
n.sub.0 is a refractive index on an optical axis of a fiber;
r is a distance from said optical axis;
a is a radius of the core of said fiber;
.DELTA. is a non-dimensional parameter, indicative of an index
difference between the core and a cladding of the fiber; and
.alpha. is a non-dimensional parameter, indicative of a shape of
the index profile.
When a light signal propagates in such a core having a graded
index, the different modes experience a different propagation
medium, which affects their speed of propagation differently. By
adjusting the value of the parameter .alpha., it is thus possible
to theoretically obtain a group velocity, which is virtually equal
for all the modes and thus a reduced intermodal dispersion for a
particular wavelength. However, an optimum value of the parameter
.alpha. is valid for a particular wavelength only. Furthermore, the
exact parameter value .alpha., as well as the actual shape of the
refractive index profile, are difficult to control during
manufacture of the fiber.
It is thus important to take account of modal dispersion when
assessing the effective bandwidth of a multimode optical fiber
link.
As mentioned above, the Effective Bandwidth is also affected by the
chromatic dispersion, also called material dispersion. Chromatic
dispersion occurs because the refractive index of a material
changes with the wavelength of light. As a consequence, different
wavelengths travel at different speeds in a multimode fiber. Since
a pulse of light typically comprises several wavelengths, the
spectral components of the optical signal spread in time, or
disperse, as they propagate, causing the pulse width to broaden. A
multimode fiber typically has a chromatic dispersion of the order
of -100 ps/nm-km at a wavelength of 850 nm. The chromatic
dispersion can vary between -80 and -120 ps/nm-km in the spectral
range 840-860 nm.
Originally, modal and chromatic dispersions have been assumed to
act independently. As a consequence, the Effective Bandwidth (EB),
which corresponds to the bandwidth of the fiber when both the modal
dispersion and the chromatic dispersion are taken into account, has
long been assessed as the result of an independent combination of
the Effective Modal Bandwidth (EMB), which corresponds to the
bandwidth of the source-fiber pair when the chromatic dispersion is
disregarded, and a Chromatic Dispersion Bandwidth (BWch).
More precisely, the Chromatic Dispersion Bandwidth is determined
from the spectral width for the VCSEL, by taking account of the
nominal value of the chromatic dispersion of the fiber. Actually,
the chromatic dispersion is considered as not varying so much from
fiber to fiber.
The Chromatic Dispersion Bandwidth is hence calculated as
follows:
.sigma..times..times..times..times..lamda..lamda..lamda..times..times..ti-
mes..times..sigma. ##EQU00002##
where:
L is the link length in kilometers;
.sigma. is the root mean square (rms) optical spectral width of the
laser source in nm;
.lamda..sub.0 is the wavelength of zero dispersion of the fiber in
nm;
.lamda..sub.c is the center wavelength of the laser;
S.sub.0 is the dispersion parameter of the fiber in
ps/(kmnm).sup.2.
As regards Effective Modal Bandwidth, it is usually estimated by a
measurement of the delay due to the modal dispersion, known under
the acronym DMD for "Dispersion Modal Delay" graphical
representation. The DMD measurement procedure has been the subject
of standardization (IEC 60793-1-49 and FOTP-220) and is also
specified in Telecommunications Industry Association Document no.
TIA-455-220-A. The DMD metric is expressed in units of picoseconds
per meter (ps/m) so that the total delay is normalized by fiber
length. Low modal dispersion as measured by DMD generally results
in higher-bandwidth MMF.
A DMD graphical representation is obtained by injecting a light
pulse having a given wavelength .lamda..sub.0 at the center of the
fiber and by measuring the pulse delay after a given fiber length
L; the introduction of the light pulse of given wavelength
.lamda..sub.0 being radially offset to cover the entire core of the
multimode fiber.
Once the Effective Modal Bandwidth and the Chromatic Dispersion
Bandwidth have been assessed, the total bandwidth, also called
Effective Bandwidth is calculated as follows:
##EQU00003##
However, for relatively long reach and at high bit rate, and
especially in case of transversally multimode sources, source and
fiber do not drive the system performance independently, because of
Modal and Chromatic Dispersion Interactions (MCDI).
Actually, the sources used in optical transmission systems are
generally not monochromatic. Thus, the widely used VCSELs have a
wide-spectrum discrete emission. The VCSELs used for high-speed
transmissions are generally longitudinally but not transversally
single mode, each transverse mode of the laser having its own
wavelength corresponding to the various peaks of the emission
spectrum. The emission spectrum thus has a spatial dependence.
When the optical signal emitted by the VCSEL is introduced into the
multimode fiber, each transverse mode of the VCSEL will diffract
differently: the transverse modes of the highest order diverge more
rapidly due to their phase and the spatial distribution of their
energy, they will therefore be coupled more specifically in the
high order modes of the fiber. It will be recalled that the high
order modes of the VCSEL occupy the lowest wavelengths in the
spectrum. This spectral and spatial distribution of the VCSEL modes
results in the highest order modes of the fibers mostly carrying
the lowest wavelengths in the spectrum: the chromatic dispersion
will therefore further delay the higher order modes relative to the
delay of the fundamental mode.
The chromatic dispersion will thus introduce a modal dispersion
referred to by the acronym MCDI for "Modal and Chromatic Dispersion
Interferences", resulting in a limitation of the bandwidth.
Document US 2011/0054861 A1 stresses the fact that the currently
standardized algorithms for determining DMD and EMB, though
adequate for appraising the quantitative amount of modal dispersion
of a particular fiber at a particular measurement wavelength, do
not correctly address both modal and chromatic dispersion effects,
and discloses an improved algorithm for calculating the bandwidth
of a particular laser transmitter and fiber combination, aiming at
correctly combining both modal and chromatic dispersion
effects.
According to this prior art document, a total bandwidth accounting
for both chromatic and modal dispersions is assessed through the
computation of a transfer function H.sub.fiber(f,n), determined by
deconvolving the launch reference pulse R(t) used in the DMD
measurements, from the output temporal responses P.sub.cd(t,n), as
follows: H.sub.fiber(f,n)=FT{P.sub.cd(t,n)}/FT{R(t)} with
P.sub.cd(t,n)=.SIGMA..sub.rD.sub.cd(r,t,n)=U.sub.cd(r,t)W(r,n) and
U.sub.cd(r,t)=FT.sup.-1{FT{U(r,t)}H.sub.cd(f,r)}
where U(r,t) are the temporal responses of the multimode fiber
optical cable, measured using spectrally narrow and temporally
short pulses of light with central wavelength .lamda..sub.c,
injected into a core of the multimode fiber optic cable at series
of radial offsets r from the core,
and where U.sub.cd(f,r) is the chromatic dispersion transfer
function calculated at the radial offset r from the Time Of Flight
TOF(.lamda.) and the optical spectrum of the transceiver measured
at offset r L (.lamda.,r):
H.sub.cd(f,r)=FT{L(.lamda.,r)TOF(.lamda.)}.
Although it attempts to take account of both modal and chromatic
dispersion for characterizing a multimode fiber system, such a
method shows several drawbacks.
First, such a method does not differentiate between the source
characterization and the fiber characterization.
Secondly, such a method does not disclose how to use the source and
fiber metrics to derive the Effective Bandwidth of a multimode
optical fiber link, but only allows determining a bandwidth range,
and perhaps a minimum bandwidth of a fiber and a population of
laser transmitters.
Yet, the Effective Bandwidth value of a multimode optical fiber
link is very useful to optimize the system performance, to assess
its reach, to assess power penalties or a maximum bit rate
achievable for example.
It would hence be desirable to have an improved method for
assessing the effective bandwidth of a system comprising a source
and a multimode fiber, which would take account of both chromatic
and modal dispersion effects.
It would also be desirable to have such a method that does not
require in situ measurements. It would also be desirable to obtain
new metrics that would characterize the source and the multimode
fiber, and that could be used to predict system performances.
3. SUMMARY
In one aspect, a method of characterizing a multimode optical fiber
link comprising a light source and at least one multimode fiber is
provided. Such a method comprises a step of characterizing the
multimode fiber using a measurement of the Dispersion Modal Delay
(DMD) and delivering fiber characteristic data. Such a method also
comprises: a step of characterizing the light source by at least
three source characteristic curves obtained by: exciting a nominal
multimode fiber with the light source; scanning with a single mode
fiber an output signal of the nominal multimode fiber, at different
radial offset values r, from an axis of said nominal fiber where
r=0 to a radial offset value r=a, where a is the core radius of the
nominal fiber, analyzing with a spectrum analyzer an output optical
spectrum of the single mode fiber for each radial offset value r,
the source characteristic curves each showing a source parameter as
a function of the radial offset value r; a step of computing an
Effective Bandwidth (EB) of the link, comprising calculating a
transfer function using both the fiber characteristic data and each
of the source characteristic curves.
The invention thus relies on a new and inventive approach of the
characterization of multimode optical fiber links. It is actually
based on the finding that source and fiber do interact on the
system performance, and that it is thus not reliable to compute
separately the Effective Modal Bandwidth and the Chromatic
Dispersion Bandwidth to take account of both the modal and
chromatic dispersion phenomena.
The method according to an embodiment of the invention allows
isolating the relevant metrics that characterize the source and the
fiber, and provides a new way of processing them to assess the
Effective Bandwidth of the optical link. In other words, according
to such a method, the fiber and the source can be characterized
separately, without the need to make the link physically to assess
its potential. Yet, the interaction between modal and chromatic
dispersions is restored.
The characterization of the source relies on a new technique, which
is somehow similar in its approach to the DMD measurement technique
as specified in IEC 60793-1-49 and FOTP-220 standards. The
characterization of the multimode fiber relies on this standardized
DMD measurement technique.
Such a method for characterizing a multimode optical fiber link can
advantageously be used in the framework of fiber manufacturing to
support a method of qualifying fibers offering a minimal EB for a
given set of transceivers. It may also be used for qualifying the
effect of additional active or passive components inserted in a
link, through the monitoring of their effect on the source and/or
fiber metrics, as well as the consequences on the Effective
Bandwidth of a link.
Moreover, this method is not limited to the 840-860 nm wavelength
range, and can be applied for sources emitting over the whole
available spectrum range available for data communications with
optical fibers, for instance over the 633-1625 nm range and even
beyond 1625 nm, around 2 .mu.m for instance. It is not either
limited to VCSEL based sources, and can be used with DFB (for
"Distributed FeedBack") lasers, LED (for "Light Emitting Diodes")
or Silicon Photonic sources for instance. It is particularly suited
to spectrally wide sources, transversally and/or longitudinally
multimode sources.
Moreover, this method is not limited to 50 .mu.m graded-index
multimode fibers: it can be applied to smaller core diameters from
10 to 50 .mu.m or larger core diameters from 50 to 100 .mu.m for
instance. Moreover, this method is not limited to graded-index
multimode fibers and is particularly suited to any fiber sustaining
more than one mode at the operating wavelengths of interest.
As used herein multimode optical fiber is an optical fiber able to
transmit more than one mode at the intended operating
wavelengths.
In another aspect, said source characteristic curves comprise: a
curve showing an output power P(r) of said source as a function of
said radial offset value r, 0.ltoreq.r.ltoreq.a; a curve showing a
center wavelength .lamda..sub.c(r) of said source as a function of
said radial offset value r, 0.ltoreq.r.ltoreq.a; a curve showing a
root mean square spectral width .DELTA..lamda.(r) of said source as
a function of said radial offset value r, 0.ltoreq.r.ltoreq.a.
The method according to an embodiment of the invention thus
advantageously avoids the use of the full optical spectrum. It
rather only considers the center wavelength .lamda..sub.c(r) and
the spectral width RMS .DELTA..lamda.(r) of the source. The
inventors have actually demonstrated that such a method was
sufficient to reach good results, which was far from being obvious,
given the complexity of the spectrum shape.
Moreover, the method according to an embodiment of the invention
advantageously uses the metric .DELTA..lamda.(r) for characterizing
the source, which is critical since it provides the right scaling
of the resulting Effective Bandwidth that is mandatory for system
margin calculations.
Advantageously, said nominal multimode fiber exhibits a length
close to said link length. The characterization of the source is
thus carried out in conditions similar to the actual optical
link.
According to an aspect of the invention, said step of
characterizing said multimode fiber and said step of characterizing
said light source use the same single mode fiber, so as to avoid
any discrepancy between the characterization of the source and of
the fiber which would be induced by the use of different single
mode fibers.
In a first particular embodiment of the invention, said step of
computing an Effective Bandwidth (EB) of said link derives said
Effective Bandwidth from a transfer function H(f): where
.function..times..times..function..function..function..function..pi..DELT-
A..tau..function..times..sigma..function. ##EQU00004## with:
.DELTA..tau..function..lamda..function..lamda. ##EQU00005##
.sigma..function..DELTA..lamda..function..times. ##EQU00005.2##
where:
{tilde over (s)}.sub.DMD(r,f) and {tilde over (s)}.sub.ref(f) are
the Fourier transform of s.sub.DMD(r,t) and s.sub.ref (t),
L and L.sub.DMD are the multimode fiber length in said link and the
multimode fiber length in DMD measurements respectively,
D is the chromatic dispersion of said nominal fiber expressed in
ps/nm-km,
.lamda..sub.DMD is the wavelength of said measurement of the
Dispersion Modal Delay,
s.sub.DMD(r,t) is a DMD trace at radial offset value r,
s.sub.ref(t) is a reference pulse signal,
and OMBc(r) is the OMBc (for "Overfilled Modal Bandwidth
calculated") weight function. As an example, the Effective
Bandwidth is calculated as the bandwidth at -3 dB of the H(f)
transfer function, such that:
.times..function..function. ##EQU00006## Of course, other ways of
deriving EB from H(f) could be used, such as by using a -1.5 dB
threshold and multiplying the obtained bandwidth by 2, or by using
a -6 dB threshold for example.
According to this first embodiment of the invention, the multimode
fiber is characterized by using the full DMD plot.
The OMBc weight functions are the weight functions that correspond
to over-filled launch as disclosed in "Calculated Modal Bandwidths
of an OMA Fiber and the Theoretical Challenges" by Abhijit
Sengupta, International Wire & Cable Symposium, Proceedings of
the 58.sup.th IWCS/IICIT, pp. 24-29 for 50 .mu.m graded-index MMFs.
Note that the OMBc weight functions can be calculated for any
refractive index profile and must be adapted to the nominal fiber
profile.
According to a second particular embodiment of the invention, said
step of characterizing said multimode fiber comprises a step of
calculating at least three fiber characteristic curves from said
measurement of said Dispersion Modal Delay, said fiber
characteristic curves comprising: a curve showing a Radial Offset
Bandwidth ROB(r) of said multimode fiber as a function of said
radial offset value r, 0.ltoreq.r.ltoreq.a; a curve showing a
Radial Offset Delay ROD(r) of said multimode fiber as a function of
said radial offset value r, 0.ltoreq.r.ltoreq.a; a curve showing a
Radial Coupling Power P.sub.DMD(r) of said multimode fiber as a
function of said radial offset value r, 0.ltoreq.r.ltoreq.a.
According to this second embodiment, the characterization of the
multimode fiber uses relevant metrics extracted from the DMD plot,
that are more simple and convenient to use, with minor lose of
accuracy compared to the above first embodiment. The Radial Offset
Bandwidth ROB(r) and the Radial Offset Delay ROD(r) are normalized
to the fiber length used in the DMD measurements and are typically
and respectively expressed in MHzkm and ps/m.
According to an aspect of this second embodiment, said step of
computing an Effective Bandwidth (EB) of said link derives said
Effective Bandwidth from a transfer function H(f):
where
.function..times..function..function..function..times..times..times..time-
s..pi..function..DELTA..times..times..tau..function..DELTA..times..times..-
tau..function..times..sigma..function..sigma..function.
##EQU00007## with:
.DELTA..times..times..tau..function..lamda..function..lamda.
##EQU00008##
.sigma..function..DELTA..times..times..lamda..function..times.
##EQU00008.2##
.DELTA..times..times..tau..function..intg..function..intg..function..abou-
t..times..times..times..times..function. ##EQU00008.3##
.sigma..function..times..times..times..times..function..times.
##EQU00008.4## where:
L is the multimode fiber length in said link,
L.sub.DMD is a length of multimode fiber used in said measurement
of the Dispersion Modal Delay,
D is the chromatic dispersion of said nominal fiber expressed in
ps/nm-km,
.lamda..sub.DMD is the wavelength of said measurement of the
Dispersion Modal Delay,
s.sub.DMD(r,t) is a DMD trace at radial offset value r,
and OMBc(r) is the OMBc (for "Overfilled Modal Bandwidth
calculated") weight function.
As an example, the Effective Bandwidth is calculated as the
bandwidth at -3 dB of the H(f) transfer function, such that:
.times..function..function. ##EQU00009## or course, other ways of
deriving EB from H(f) could be used, such as by using a -1.5 dB
threshold and multiplying the obtained bandwidth by 2, or by using
a -6 dB threshold for example.
It should be noted that s.sub.DMD(r,t) and s.sub.ref(t) are
normalized to the fiber length used in the DMD measurements
L.sub.DMD, and the t argument in s.sub.DMD t) and s.sub.ref(t) is
thus expressed in s/m. The OMBc weight functions are the weight
functions disclosed in "Calculated Modal Bandwidths of an OM4 Fiber
and the Theoretical Challenges" by Abhijit Sengupta, International
Wire & Cable Symposium, Proceedings of the 58.sup.th
IWCS/IICIT, pp. 24-29, but tuned to account for the refractive
index profile of the nominal fiber.
According to another embodiment of the invention, said chromatic
dispersion D in .DELTA..tau.(r) is replaced by a function of the
radius D(r), such that:
.DELTA..tau.(r)=LD(r)(.lamda..sub.c(r)-.lamda.DMD).
Actually, both methods described above in relation to the first and
second embodiments of the invention work fine when .lamda..sub.c(r)
is close to the .lamda..sub.DMD wavelength. However, some
discrepancy may occur when .lamda..sub.c(r) is too different from
the .lamda..sub.DMD wavelength. This comes from the fact that
Dispersion Modal Delay DMD varies with the operating wavelength
.lamda..sub.DMD used during the DMD measurements. To account for
this phenomenon, one can correct the transfer functions H(f) used
in both the first and second embodiments of the invention, by
modifying the chromatic dispersion D in the equation of
.DELTA..tau.(r) by a function D(r) of the radius.
Preferably, D(r)=D.sub.0+ar.sup.2+br, where D.sub.0, a and b are
coefficients calculated for example using a method belonging to the
group comprising: chromatic dispersion measurements along radius
with DMD like excitations; comparing ROD curves obtained at two
different wavelengths.
The invention also concerns a method of fabricating multimode
optical fiber links comprising a light source and a multimode
fiber, the method comprising: selecting a set of multimode optical
fibers and a set of light sources; for each multimode optical fiber
and for each light source in said sets, characterizing the
multimode optical fiber link formed with said multimode optical
fiber and said light source in compliance with the method of any of
claims 1 to 9; selecting only those multimode optical fiber links
for which the effective bandwidth EB>3000 MHz-km, more
preferably EB>4500 MHz-km, even more preferably EB>6000
MHz-km.
The invention also concerns a method of selecting multimode optical
fibers from a batch of multimode optical fibers, the method
comprising: selecting a batch of multimode optical fibers and a set
of light source metrics; for each multimode optical fiber and each
light source metric in said set, characterizing the multimode
optical fiber link formed with said multimode optical fiber and
said light source metric in compliance with the method of any of
the claims 1 to 9; selecting only those multimode optical fibers
for which the minimal calculated effective bandwidth over the whole
set of light source metrics is >3000 MHz-km, more preferably
>4500 MHz-km, even more preferably >6000 MHz-km, wherein the
set of light source metrics is obtained through measuring or
modeling a representative set of light sources.
More generally, the Effective Bandwidth computed according to the
method of characterizing a multimode optical link of the invention
can be used: To sort out/to optimize fibers for a given source or
set of sources to optimize system performance (low penalties)
and/or to extend the reach; To sort out/to optimize sources for a
given fiber or set of fibers to optimize system performance (low
penalties) and/or to extend the reach; To assess power
penalties/system margins for a given link length and bit rate; To
assess system reach for a given power penalty level/system margins
for a given bit rate; To assess maximum bit rate achievable for a
given power penalty/system margins and given link length.
4. BRIEF DESCRIPTION OF THE DRAWINGS
The invention can be better understood with reference to the
following description and drawings, given by way of example and not
limiting the scope of protection, and in which:
FIG. 1 shows an example of an optical communication system
including a multimode fiber;
FIG. 2 illustrates the DMD measurement technique;
FIG. 3 illustrates the source characterization technique according
to embodiments of the invention;
FIG. 4 shows the optical spectrum of a source characterized with
the technique of FIG. 3 in an exemplary embodiment of the
invention;
FIG. 5 illustrates the output power P(r) as a function of the
radial offset value of a source characterized with the technique of
FIG. 3 in an exemplary embodiment of the invention;
FIG. 6 depicts the center wavelength .lamda..sub.c(r) as a function
of the radial offset value of a source characterized with the
technique of FIG. 3 in an exemplary embodiment of the
invention;
FIG. 7 illustrates the root mean square spectral width
.DELTA..lamda.(r) as a function of the radial offset value of a
source characterized with the technique of FIG. 3 in an exemplary
embodiment of the invention;
FIG. 8 illustrates the OMBc weight function used in an exemplary
embodiment of the invention;
FIG. 9 shows a comparison of a theoretical Effective Bandwidth, and
of an Effective Bandwidth computed according two embodiments of the
invention, as well as Effective Bandwidths computed according to
prior art technique;
FIG. 10 illustrates the importance for characterizing the source of
the source metrics .lamda..sub.c(r) and .DELTA..lamda.(r) derived
according to embodiments of the invention, as well as their
influence on the computation of the Effective Bandwidth of an
optical link;
FIG. 11 shows a comparison between the theoretical Effective
Bandwidth, and the EB3 Effective Bandwidth computed according to
the first and second embodiments of the invention;
FIGS. 12A, 12B and 12C correspond to the curves of FIGS. 5, 6 and 7
for another exemplary embodiment of the invention;
FIG. 13 illustrates the DMD plot obtained through the DMD
measurement technique for the multimode fiber of the exemplary
embodiment of FIGS. 12A-12C;
FIG. 14 compares the Effective Bandwidth expressed in MHz-km
obtained through different methods for the optical link of the
exemplary embodiment of FIGS. 12A-12C;
FIGS. 15 and 16 both focus on an enhanced embodiment of the
invention;
FIG. 17 shows a synoptic diagram of the method of characterizing a
multimode optical fiber link according to the invention;
FIG. 18 shows an example of DMD plot resulting from a DMD
measurement for a multimode fiber characterized according to an
embodiment of the invention;
FIG. 19 illustrates the ROB curve derived from the DMD plot of FIG.
18;
FIG. 20 illustrates the ROD curve derived from the DMD plot of FIG.
18;
FIG. 21 illustrates the P.sub.DMD curve derived from the DMD plot
of FIG. 18.
The components in the figures are not necessarily to scale,
emphasis instead being placed upon illustrating the principles of
the invention.
5. DETAILED DESCRIPTION
The general principle of the invention relies on separate source
and fiber characterizations, allowing isolating the relevant
metrics that characterize both the source and the fiber, and a new
method for assessing the Effective Bandwidth, starting from these
new metrics.
FIG. 17 illustrates by a synoptic diagram the method of
characterizing a multimode optical fiber link according to the
invention. Such a method relies on a characterization 170 of the
multimode fiber using a DMD measurement technique. According to
embodiments of the invention, as will appear more clearly in the
foregoing, the fiber characteristic data are either the DMD plot
itself (method 1, also referred to as the first embodiment of the
invention), or three fiber characteristic curves derived from the
DMD plot (method 2, also referred to as the second embodiment of
the invention).
Such a method also relies on a separate characterization 171 of the
source, using a technique similar to the DMD measurement technique,
which allows obtaining three source characteristic curves.
Both the fiber characteristic data delivered by step 170 and the
source characteristic curves delivered by step 171 feed a computing
step 172 for computing a transfer function H(f). In a step 173, the
Effective Bandwidth of the multimode optical fiber link is then
derived from the transfer function H(f).
All these steps will be described in more details below in relation
to the other figures.
FIG. 1 shows an example of an optical communication system
including a multimode fiber, which is an exemplary subject of the
present effective bandwidth computing method. A multi Gigabits
Ethernet optical communication system successively comprises a
driver 8 of a transmitter 1, a VCSEL source 9 of a transmitter 1, a
launch cord 2, a connector 3, a multimode fiber 4, a connector 3, a
launch cord 2, a PIN diode 6 of a receiver 5, an amplifier 7 of a
receiver 5. A digital signal at 10 Gbps or 25 Gbps is generated by
the driver 8, which directly modulates the VCSEL source 9.
For sake of simplification, we hereafter consider only one
multimode fiber; however, the general principles described below
will be easily extended to the case where several multimode fibers
are concatenated to form a link.
According to embodiments of the invention, the multimode fiber 4
characterization is mainly based on the DMD measurements, as
described in the standard TIA FOTP-220 or IEC 60793-1-49
(TIA-455-220-A, "Differential Mode Delay Measurement of Multimode
Fiber in the Time Domain" (January 2003)).
FIG. 2 illustrates the DMD measurement technique. An ultrafast
laser pulse is launched into a multimode fiber MMF using a single
mode fiber SMF. The SMF is scanned radially, and for each radial
offset position, the shape of the transmitted pulse is recorded
using a high bandwidth optical receiver 30 and a sampling
oscilloscope.
More precisely, an optical reference pulse s.sub.ref(t) at 850 nm
is emitted by a source and launched into the core 10 of a
single-mode launch fiber SMF, with a core diameter of 5 .mu.m. From
the end of the SMF, it is stepped across the core 20 of a multimode
fiber MMF under test. Such a MMF has typically a core diameter of
50 .mu.m. For each lateral offset across the core (0 to 24
microns), the propagation delay of the resultant output pulse is
recorded. Each output pulse contains only those modes excited at a
given input radial position. The output waveforms for each of the
radial offsets are plotted along the vertical axis and are
displaced by 1-micron increments, as shown on the right part of
FIG. 2, also called a DMD plot. The relative pulse delay for each
waveform is plotted along the horizontal axis in units of
picoseconds per meter (ps/m). The DMD is determined by first
measuring the difference pulse in delay using the leading edge of
the fastest pulse and the trailing edge of the slowest pulse. From
this difference we subtract the temporal width of the launch pulse,
which yields the modal dispersion of the fiber.
FIG. 3 illustrates the source characterization technique according
to embodiments of the invention. This characterization is similar
to that of the DMD measurement technique.
A nominal multimode graded-index fiber, with a core 31 showing a
diameter of 50 .mu.m, is first excited with the source to be
characterized. Such a nominal multimode graded-index fiber has
sensibly the same core diameter, numerical aperture and single
alpha graded index profile as the multimode fiber used in the link.
A single mode fiber 32 scans the output of the nominal fiber, in a
manner similar to that used in the standard DMD measurements, thus
preferably from 0 to 25 .mu.m, with a 1-micron step. An optical
spectrum analyzer 30 placed at the output of the single mode fiber
32 records the output optical spectrum for each position of the
SMF.
Without lack of generality, the single mode fiber 32 used for the
source characterization may be the same as the single mode fiber 10
used for the fiber characterization.
Although not illustrated on FIG. 3, such a technique allows
collecting a series of optical spectra, which have to be
post-processed, so as to generate three source characteristic
curves, namely: a curve showing an output power P(r) of the source
as a function of the radial offset value r of the SMF 32,
0.ltoreq.r.ltoreq.a. Such a power may be expressed as a relative
power; a curve showing a center wavelength .lamda..sub.c(r) of the
source as a function of the radial offset value r of the SMF 32,
0.ltoreq.r.ltoreq.a; a curve showing a root mean square spectral
width .DELTA..lamda.(r) of said source as a function of the radial
offset value r of the SMF 32, 0.ltoreq.r.ltoreq.a, where a is the
core radius of the multimode nominal fiber 31.
In a first exemplary embodiment of the invention, the inventors
have simulated the coupling between a transversally multimode (and
longitudinally single mode) laser into a 50 .mu.m graded-index
multimode fiber. As shown in FIG. 4, such a source exhibits nine
mode groups, named MG1 to MG9. As can be read on FIG. 4, the center
wavelength .lamda..sub.c is 850.0 nm, and the spectral width RMS is
0.35 nm. The waist of laser (i.e. the spot radius of the
fundamental mode) is 3 .mu.m. The position of the source with
respect to the nominal multimode fiber 31 is arbitrarily chosen.
The resulting insertion loss is less than 0.25 dB. The resulting
encircled flux at the output of single-mode fiber 32 is 17.1 .mu.m
86% EF radius & 15.8% EF at 4.5 .mu.m.
FIGS. 5, 6 and 7 illustrate the three curves that characterize the
source-fiber coupling, according to the technique of FIG. 3: more
precisely, FIG. 5 illustrates the output power P(r) of the source
as a function of the radial offset value; FIG. 6 illustrates the
center wavelength .lamda..sub.c(r) of the source as a function of
the radial offset value; FIG. 7 depicts the root mean square
spectral width .DELTA..lamda.(r) of the source as a function of the
radial offset value. It is interesting to note that the RMS
spectral width .DELTA..lamda.(r) also significantly varies along
the fiber core 31.
Once a DMD measurement has been carried out for characterizing the
multimode fiber under test, and once the source has been
characterized using the technique of FIG. 3, the method of the
invention proposes to compute the Effective Bandwidth of the
multimode optical fiber link.
According to a first embodiment, the Effective Bandwidth (hereafter
called EB3) is computed as the bandwidth at -3 dB of the transfer
function H(f), such that:
.times..function..times..times..function. ##EQU00010## with:
.function..times..function..function..function..function..times..times..t-
imes..times..pi..times..times..DELTA..times..times..tau..function..times..-
sigma..function. ##EQU00011##
.times..DELTA..times..times..tau..function..lamda..function..lamda.
##EQU00011.2##
.times..sigma..function..DELTA..times..times..lamda..function..times.
##EQU00011.3## where:
{tilde over (s)}.sub.DMD(r,f) and {tilde over (s)}.sub.ref(f) are
the Fourier transform of s.sub.DMD(r,t) and s.sub.f (t),
L is the multimode fiber length in said link (e.g. 500 m),
D is the chromatic dispersion of the nominal fiber expressed in
ps/nm-km (e.g. -100 ps/nm-km) (the nominal fiber has preferably the
same dopants content as the multimode fiber under test),
.lamda..sub.DMD is the wavelength of the measurement of the
Dispersion Modal Delay,
S.sub.DMD(r,t) is a DMD trace at radial offset value r,
s.sub.ref(t) is a reference pulse signal,
and OMBc(r) is the OMBc (for "Overfilled Modal Bandwidth
calculated") weight function.
More information on OMBc weight functions can be found in
"Calculated Modal Bandwidths of an OM4 Fiber and the Theoretical
Challenges" by Abhijit Sengupta, International Wire & Cable
Symposium, Proceedings of the 58.sup.th IWCS/IICIT, pp. 24-29. As
disclosed in this document, overfilled modal bandwidth calculated
(OMBc) of a multimode fiber can be predicted from the weighted
linear combination of differential modal delay data.
Actually, coupled power in each mode is calculated from the overlap
integral of a Gaussian mode field of a single mode probe fiber
(SMPF) and the specific mode of the MMF for each radial offset
position. The coupling efficiency at each radial offset is
calculated as the total coupled power summed over all modes
normalized to unit incident power. The overfilled launch source is
expressed as a linear combination of SMPF modes fields at the
radial offset positions of the DMD scan. Per the definition of OFL,
the weights for different offset positions are optimized so that
the total energy in each mode of the MMF is equal. These
theoretical DMD weighting values are tabulated to obtain the OMBc
for the DMD data measured from 0-30 microns (i.e. complete DMD
data). These weights are then adjusted to provide optimal values
for the case where the DMD data does not exist at radii higher than
25 microns.
According to a second embodiment of the invention, the Effective
Bandwidth is not calculated straight away from the DMD plot and the
three source-characteristic curves, but three curves that
characterize the multimode fiber have first to be calculated from
the DMD plot: a curve showing a Radial Offset Bandwidth ROB(r) of
the multimode fiber as a function of the radial offset value r,
0.ltoreq.r.ltoreq.a; a curve showing a Radial Offset Delay ROD(r)
of the multimode fiber as a function of the radial offset value r,
0.ltoreq.r.ltoreq.a; a curve showing a Radial Coupling Power
P.sub.DMD(r) of the multimode fiber as a function of the radial
offset value r, 0.ltoreq.r.ltoreq.a, which may be expressed as a
relative power.
The Radial Offset Bandwidth is described in several prior art
documents, among which patent document EP2207022. As described in
this patent document, the radial offset bandwidth ROB(r) is defined
as the -3 dB bandwidth of a transfer function
.function..function..function. ##EQU00012## where:
S.sub.e(f) is the Fourier transform of the time profile of the
inlet pulse s.sub.e(t), launched in the DMD measurement,
S.sub.s(f,r) is the Fourier transform of the time profile of the
outlet pulse s.sub.s(t,r) for a radial offset r, at the output of
the multimode fiber under test,
and f indicates frequency.
An interesting characteristic of the ROB is its high sensitivity to
localized defects in refractive index. Hence, if the ROB decreases
too quickly on increasing the radial offset r, then it is likely
that the fiber presents an irregular index profile.
ROB is normalized to the fiber length in the DMD measurement and is
generally expressed in MHzkm.
As regards the ROD, it corresponds to the mean temporal position of
the fiber output response for a given delay.
The ROD curve for the fiber somehow corresponds to the
.lamda..sub.c curve for the source, while the ROB curve for the
fiber somehow corresponds to the .DELTA..lamda. curve for the
source.
ROD is normalized to the fiber length used in the DMD measurements
to be expressed typically in ps/m.
FIG. 18 illustrates a DMD plot obtained by characterizing a
multimode fiber through a DMD measurement technique. FIGS. 19 to 21
show respectively the ROB curve, the ROD curve and the P.sub.DMD
curve as a function of the radial offset value derived from the DMD
plot according to the second embodiment of the invention.
Using these three fiber-characteristic curves along with the three
source-characteristic curves of FIGS. 5 to 7, the method according
to this second embodiment of the invention proposes to compute the
Effective Bandwidth (hereafter called EB3) as the bandwidth at -3
dB of the transfer function H(f), such that:
.times..function..times..times..function. ##EQU00013## with:
.function..times..function..function..function..times..times..times..time-
s..pi..function..DELTA..times..times..tau..function..DELTA..times..times..-
tau..function..times..sigma..function..sigma..function.
##EQU00014## with:
.DELTA..times..times..tau..function..lamda..function..lamda.
##EQU00015##
.sigma..function..DELTA..times..times..lamda..function..times.
##EQU00015.2##
.DELTA..times..times..tau..function..intg..function..intg..function..abou-
t..times..times..times..times..function. ##EQU00015.3##
.sigma..function..times..times..times..times..function..times.
##EQU00015.4## where:
L is the multimode fiber length in the link (e.g. 500 m),
L.sub.DMD is a length of multimode fiber used in the measurement of
the Dispersion Modal Delay,
D is the chromatic dispersion of the nominal fiber expressed in
ps/nm-km (e.g. -100 ps/nm-km) (the nominal fiber has preferably the
same dopants content as the fiber under test),
.lamda..sub.DMD is the wavelength of the measurement of the
Dispersion Modal Delay,
s.sub.DMD(r,t) is a DMD trace at radial offset value r,
and OMBc(r) is the OMBc (for "Overfilled Modal Bandwidth
calculated") weight function.
Referring back to the exemplary embodiment illustrated through
FIGS. 4 to 7, the theoretical Effective Bandwidth (that requires
eigenmode computations, and thus accurate knowledge of the source
and the fiber), and the EB3 Effective Bandwidth have been computed
for a few fibers. FIG. 8 illustrates the OMBc weight function used
in this exemplary embodiment.
The fibers were simulated as perfect alpha profile with alpha
varying between 2.05 and 2.08. The DMD measurement of these fibers
was also simulated. The graph on FIG. 9 reports the theoretical
Effective Bandwidth EB and the EB3 Effective Bandwidth obtained for
these fibers and for this given source as a function of alpha: the
agreement is excellent.
Referring to the caption box of FIG. 9: "theoretical EB"
corresponds to the theoretical Effective Bandwidth obtained from
eigenmode computation and accurate knowledge of the source and the
fiber; "EB3 Method 1" corresponds to the Effective Bandwidth
computed according to the first embodiment of the invention; "EB3
Method 2" corresponds to the Effective Bandwidth computed according
to the second embodiment of the invention; EB1 corresponds to the
Effective Bandwidth assessed through prior art techniques such as
those disclosed in patent documents EP2144096, U.S. Pat. No.
7,995,888, U.S. Pat. No. 8,260,103, US20100028020 or US20110293290;
EB2 corresponds to the Effective Bandwidth assessed through prior
art techniques such as those disclosed in patent documents
EP2584388 or US20130100437. Such techniques are relatively complex,
since they require an a priori knowledge of the source.
FIG. 10 illustrates the importance for characterizing the source of
the source metrics .lamda..sub.c(r) and .DELTA..lamda.(r) derived
according to embodiments of the invention, as well as their
influence on the computation of the Effective Bandwidth of an
optical link. Actually, referring to the caption box of FIG. 10:
"theoretical EB" corresponds to the theoretical Effective Bandwidth
obtained from eigenmode computation and accurate knowledge of the
source and the fiber; "EB3 Method 1" corresponds to the Effective
Bandwidth computed according to the first embodiment of the
invention; "EBc3 (RMS=0)" corresponds to the Effective Bandwidth
computed according to the first embodiment of the invention, but by
neglecting the RMS spectral width of the source
(.DELTA..lamda.(r)=0); "EBc3 (RMS=0 Tau=0)" corresponds to the
Effective Bandwidth computed according to the first embodiment of
the invention, but by neglecting both the RMS spectral width of the
source (.DELTA..lamda.(r)=0) and the central wavelength
distribution of the source (.lamda..sub.c(0=0); "EBc3 (Tau=0)"
corresponds to the Effective Bandwidth computed according to the
first embodiment of the invention, but by neglecting the central
wavelength distribution of the source (.lamda..sub.c(r)=0).
The inventors have simulated a plurality of links using the method
of characterizing a multimode fiber link according to the first and
second embodiments of the invention. FIG. 11 shows a comparison
between the theoretical Effective Bandwidth, and the EB3 Effective
Bandwidth computed according to the first and second embodiments of
the invention. As can be observed, both computations of EB3 provide
results, which are close to the theoretical EB.
FIGS. 12A-12C to FIG. 14 show another exemplary embodiment of the
invention, which illustrates that the third source characteristic
curve showing the RMS spectral width as a function of the radial
offset value is critical for the assessment of the total bandwidth
EB3.
FIGS. 12A to 12C respectively show: a curve of the output power
P(r) as a function of the radial offset value of a VCSEL source; a
curve of the center wavelength .lamda..sub.c(r) as a function of
the radial offset value of this VCSEL source; a curve of the root
mean square spectral width .DELTA..lamda.(r) as a function of the
radial offset value of this VCSEL source.
FIG. 13 illustrates the DMD plot obtained through the DMD
measurement technique for the multimode fiber of this exemplary
embodiment.
FIG. 14 compares the Effective Bandwidth expressed in MHz-km
obtained for the optical link of this exemplary embodiment: through
calculation of a theoretical EB; through calculation of the
Effective Bandwidth EB3 according to the first embodiment of the
invention; through calculation of the Effective Bandwidth EB3
according to the second embodiment of the invention; through
calculation of the Effective Bandwidth EB3 according to the first
embodiment of the invention, by using the 0.35 nm RMS spectral
width instead of the complete third curve .DELTA..lamda.(r) of FIG.
12C.
As can be observed, the Effective Bandwidth of the optical link is
significantly overestimated of roughly 15%, when a 0.35 nm RMS
spectral width is used instead of the complete third curve
.DELTA..lamda.(r) of FIG. 12C.
FIGS. 15 and 16 both focus on an enhanced embodiment of the
invention.
Actually, both methods described above in relation to the first and
second embodiments of the invention work fine when .lamda..sub.c(r)
is close to the .lamda..sub.DMD) wavelength. However, some
discrepancy may occur when .lamda..sub.c(r) is too different from
the .lamda..sub.DMD wavelength. This comes from the fact that
Dispersion Modal Delay DMD varies with the operating wavelength
.lamda..sub.DMD) used during the DMD measurements. To account for
this phenomenon, one can correct the transfer functions H(f) used
in both the first and second embodiments of the invention, by
modifying the chromatic dispersion D in the equation of
.DELTA..tau.(r) by a function D(r) of the radius.
More precisely, it is possible to replace
.DELTA..tau.(r)=LD(.lamda..sub.c(r)-.sub.DMD) with
.DELTA..tau.(r)=LD(r)(A.sub.c(r)-.lamda..sub.DMD). Typically, a
polynomial of order 2 may be used: D(r)=D.sub.0+ar.sup.2+br.
For instance, for a 50 .mu.m graded-index multimode fiber, we can
use: a=5.10.sup.-3 ps/nm-km-.mu.m.sup.2 b=-3.42.10.sup.-4
ps/nm-km-.mu.m D.sub.0=-91.85 ps/nm-km
These coefficients can be calculated through chromatic dispersion
measurements along radius with DMD like excitation, or with the
comparison of ROD curves obtained at two different wavelengths
.lamda..sub.1 and .lamda..sub.2.
The curve on FIG. 15 reports
.times..times..times..times..function..lamda..times..times..times..times.-
.function..lamda..lamda..lamda. ##EQU00016## FIG. 16 shows the
chromatic dispersion D(r) as a function of radius r. Coefficients
a, b, and D.sub.0 may depend on the manufacturing process of the
fiber or on the dopant content of the fiber.
The method according to embodiments of the invention allow
isolating and extracting the relevant information for
characterizing both a source and a multimode fiber, into a single
set of curves for the source and into a single set of curves for
the fiber. A standardized used of such a method would hence
considerably simplify sorting method and/or link engineering, and
make easier the collaboration between source and fiber
manufacturers.
* * * * *